Details

Time bar (total: 9.4s)

sample69.0ms

Algorithm
intervals
Results
24.0ms55×body1280valid
17.0ms45×body640valid
10.0ms132×body80valid
3.0ms15×body320valid
1.0ms9×body160valid

simplify45.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17513
213913
320713
437513
5137313
6500113

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 17.9b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
17×add-sqr-sqrt
15×*-un-lft-identity
12×prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×unpow-prod-down sqrt-prod
4×expm1-log1p-u sqrt-div pow-exp log1p-expm1-u add-log-exp
3×pow-unpow times-frac div-exp hypot-def
2×flip3-+ associate-*r/ associate-*l* *-commutative flip-+ distribute-lft-out sqr-pow
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv
Counts
4 → 96
Calls
4 calls:
5.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
7.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
13.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series515.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
130.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
189.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
145.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify59.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04641076
11988966
25001965

prune309.0ms

Filtered
108 candidates to 73 candidates (67.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1008108
Fresh000
Picked101
Done000
Total1018109

Merged error: 6.4b

Counts
109 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b
(* (* 2.0 J) (cos (/ K 2.0)))
0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
6.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
23×pow1
15×prod-exp cbrt-unprod
12×pow-prod-down
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp associate-*l* *-commutative associate-/l*
1×frac-2neg clear-num associate-/r* div-inv
Counts
4 → 88
Calls
4 calls:
6.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
5.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
5.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
6.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series680.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
50.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
45.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
496.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify64.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0489993
12344770
25001770

prune288.0ms

Filtered
100 candidates to 66 candidates (66.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New973100
Fresh347
Picked011
Done000
Total1008108

Merged error: 6.4b

Counts
108 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
0.1b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
6.2b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.2b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1
27×add-exp-log add-cbrt-cube
16×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt associate-*r* sqrt-prod
10×add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 85
Calls
4 calls:
10.0ms
(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
7.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series2.0s

Counts
4 → 12
Calls
4 calls:
500.0ms
(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
548.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
494.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
488.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify64.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
03991874
118301509
250021503

prune350.0ms

Filtered
97 candidates to 64 candidates (66.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New95297
Fresh066
Picked011
Done011
Total9510105

Merged error: 6.4b

Counts
105 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
0.2b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
6.2b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.2b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
36×pow1
34×add-exp-log add-cbrt-cube
21×pow-prod-down prod-exp cbrt-unprod
10×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 86
Calls
4 calls:
10.0ms
(* (* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
7.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
5.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series2.1s

Counts
4 → 12
Calls
4 calls:
496.0ms
(* (* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
554.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
496.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
540.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify60.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
03982029
117601595
250011525

prune300.0ms

Filtered
98 candidates to 62 candidates (63.3%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New97198
Fresh077
Picked011
Done022
Total9711108

Merged error: 6.4b

Counts
108 → 11

regimes340.0ms

Accuracy

0% (0.3b remaining)

Error of 8.1b against oracle of 7.8b and baseline of 8.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02414
12414

end0.0ms

sample2.0s

Algorithm
intervals
Results
836.0ms1414×body1280valid
396.0ms1252×body640valid
342.0ms4421×body80valid
152.0ms624×body320valid
45.0ms289×body160valid